Weston Street in Huntington Station, which had been the site of a snaking line of residents waiting for gas on Sunday, was filled with voters' cars Tuesday morning.
Turnout was brisk at the South Huntington School District administration building on Weston Street, but waits were minimal. Most of the neighborhood still lacked power because of superstorm Sandy, but poll workers said the outage didn't appear to keep people away.
Signs for state Assembly candidates -- Joe Dujmic and Chad Lupinacci -- lined streets around the polling place. The candidates are running to fill a vacancy left by the death of 24-year assembly member Jim Conte.
Polling places opened at 6 a.m. Tuesday across Long Island, a day after Gov. Andrew M. Cuomo signed an order saying voters displaced by superstorm Sandy can cast ballots at any polling station in New York State.
Under the order, voters would sign affidavits that they are legally registered and vote at any open polling site, though voters who have relocated outside their local election districts may be limited to casting ballots only in the presidential and U.S. Senate elections.
The governor called it a trade-off.
"We want everyone to vote. Just because you are displaced doesn't mean you should be disenfranchised," the governor said. "But in the local races, if you vote in a different Assembly district, a different Senate district, your vote will not count in that district. That is the downside to the system."
Local election officials say everyone in Nassau and Suffolk will be able to vote in their local district, and are urging them to vote at their home polling places if possible. Officials have relocated some polling places in the wake of the storm and will install generators at others that are without power.
Some good-government groups applauded Cuomo's move to allow provisional voting.
Neal Rosenstein, of the New York Public Interest Research Group, a nonprofit government watchdog, said Cuomo's order "will mean increased participation in the face of great challenges faced by so many voters because of the storm."
But others said it could be difficult to check all provisional ballots later to ensure the validity of votes.
"It's a well-intentioned move but it adds confusion to an already chaotic situation," said Dick Dadey, executive director of Citizens Union. "People will show up, thinking they can vote in all the contests and they might not be able to do so."
Dadey said the expansion of provisional voting could hurt participation in congressional and legislative elections and is likely to spark lawsuits. He also said it will put a "very labor intensive" burden on already overworked local election boards to validate affidavit ballots.
New Jersey is allowing displaced voters to cast provisional ballots in polling stations other than their regularly assigned sites.
"There are just too many security risks to the validity of the election," said Doug Kellner, co-chairman of the New York State Board of Elections.
Talking generally about voting Tuesday, Cuomo said: "It's not going to be easy. But look at it this way, compared to what we've had to deal with in the past week, this is going to be a walk in the park -- going out and voting."
With Patrick Whittle